Abstract:
In this paper,
we study whether
the set
$A(\varphi)$
is closed
under multiplication
$f\cdot g$,
where
$f$
and $g$
belong
to
the class
$A(\varphi)$.
We also study
the problem of the existence of a solution
of the equation
$Bx=\nobreak C$
(where
$B,C\in A(\varphi)$
and
$B\neq \nobreak 0$)
on
the set
$A(\varphi)$.
Keywords:the class $A(\varphi)$, Banach space, Khinchine's inequality, Rademacher function, Haar system, Walsh system, Fourier coefficients.
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